Originally Posted by

**masters** Once upon a time, and old lady went to sell her vast quantity of eggs at the local market.

When asked how many she had, she replied:

Son, I can't count past 100 but I know that.

If you divide the number of eggs by 2 there will be one egg left.

If you divide the number of eggs by 3 there will be one egg left.

If you divide the number of eggs by 4 there will be one egg left.

If you divide the number of eggs by 5 there will be one egg left.

If you divide the number of eggs by 6 there will be one egg left.

If you divide the number of eggs by 7 there will be one egg left.

If you divide the number of eggs by 8 there will be one egg left.

If you divide the number of eggs by 9 there will be one egg left.

If you divide the number of eggs by 10 there will be one egg left.

Finally. If you divide the number of eggs by 11 there will be NO EGGS left!

How many eggs did the old lady have?

Hi **masters**.

The minimum number of eggs is 25201, but she could also have had 52921, 80641, 108361, …

In general:

$\displaystyle \fbox{$27720n-2519$}$ for all $\displaystyle n\in\mathbb Z^+$